Answer :
Explanation:
[tex]x + y = 3[/tex]
[tex] {x}^{2} + {y}^{2} = 29[/tex]
[tex]x = 3 - y[/tex]
[tex](3 - y) {}^{2} + {y}^{2} = 29[/tex]
[tex] {y}^{2} - 6y + 9 + {y}^{2} = 29[/tex]
[tex]2 {y}^{2} - 6y + 9 = 29[/tex]
[tex]2 {y}^{2} - 6y = 20[/tex]
[tex] {y}^{2} - 3y = 10[/tex]
[tex] {y}^{2} - 3y - 10 = 0[/tex]
[tex](y - 5)(y + 2) = 0[/tex]
[tex]y = 5[/tex]
or
[tex]y = - 2[/tex]
Plug this back in we get either that
[tex]5 + x = 3[/tex]
[tex]x = - 2[/tex]
or
[tex]x = 5[/tex]
So the numbers are
-2 and 5.